Fixed Job Scheduling with Two Types of Processors

Abstract

We consider a scheduling problem that involves two types of processors, but three types of jobs. Each job has a fixed start time and a fixed completion time, and falls into one of three types. Jobs of type 1 can be done only by type-1 processors, type-2 jobs only by type-2 processors, and type-0 jobs by either type of processors. We present a polynomial algorithm for finding the minimal cost combination of the two types of processors required to complete all jobs. The steps of the algorithm consist of constructing a job schedule network, transforming it into a single-commodity flow problem and finding the maximal flow through it.

Interval scheduling: A survey

“…As stated in Section 2.2.1, Dondeti and Emmons [26] and Huang and Lloyd [47] show that a generalization of HIS (2) is solvable in polynomial time. HIS(3), however, turns out to be hard again, as we show by a reduction from Numerical 3-Dimensional Matching (N3DM).…”

“…However, in case there are types of machines, and there is a linear order for these machine types, Bhatia et al [9] give a 2-approximation algorithm. When there are two machine-types, Dondeti and Emmons [26] and Huang and Lloyd [47] show that (a generalization of) the resulting problem is solvable in polynomial time. In Section 5, we prove that the problem becomes NPcomplete for three machine types.…”

“…In their work on interval scheduling problems, Dondeti and Emmons [26] consider a more general problem than HIS(2). They consider a variant which, in addition to jobs of type 1 and type 2, also contains jobs of type 3.…”

“…Jobs of type 3 can only be processed by machines of type 2. An important concept to decide feasibility of this problem is the so-called job schedule network; we give, in this survey, a description of this network (see [26]). …”

“…As mentioned earlier, in Ref. [26], a problem more general than HIS(2) is solved; they use a job schedule network involving O(n) nodes and O(n 2 ) arcs.…”